Many people responded to my query regarding the repertoire of vowel
phonemes in Mandarin Chinese. Some requested that I post a summary,
so here it is. I can only spare the time for a brief sketch, and
cannot credit individual respondents; this is a synthesis.
On the surface Mandarin displays about a dozen vowel segments, not
counting diphthongs. An examination of the syllable repertoire
reveals a lot of gaps, which can be explained by ascribing the surface
variety to allophony. How many underlying segments are there? A
variety of theories are possible. The pin1-yin1 spelling system is,
in essence, such a theory: several respondents who had "internalized"
this system expressed surprise that it was not necessarily perfectly
phonemic. To these respondents I recommend comparing the vowels in
the syllables "ge", "zi", and "di"; is it really clear that the latter
two are allophones, and that the former two are not? (Hint: no.)
One respondent seriously proposed a phonemic system with about a dozen
vowels; we can characterize this as a "splitter" approach.
"Conservative" accounts give five- or six-vowel systems that
approximately parallel pin1-yin1. Finally, there are "lumper"
approaches that posit only two or three underlying vowels, attributing
the concomitant rather exuberant allophony to the influence of on- and
off-glides that are then (often) removed by rule.
The only evidence available is the surface repertoire of syllables.
Mandarin doesn't have enough phonology above the syllable level to
make definite conclusions. Selecting a vowel phonology for Mandarin
remains, as far as I can tell, a matter of esthetics.
Thanks to all respondents.